NONSTANDARD ANALYSIS, FRACTAL PROPERTIES AND BROWNIAN MOTION

被引：4

作者：

Potgieter, Paul ^{[1
]}

机构：

[1] Univ S Africa, Dept Decis Sci, ZA-0003 Pretoria, South Africa

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2009年 / 17卷 / 01期

关键词：

Frostman's Lemma; Nonstandard Hausdorff Dimension; Brownian Motion;

D O I：

10.1142/S0218348X09004041

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper I explore a nonstandard formulation of Hausdorff dimension. By considering an adapted form of the counting measure formulation of Lebesgue measure, I prove a nonstandard version of Frostman's lemma and find that Hausdorff dimension can be computed through a counting argument rather than by taking the infimum of a sum of certain covers. This formulation is then applied to obtain a simple proof of the doubling of the dimension of certain sets under a Brownian motion.

引用

页码：117 / 129

页数：13

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